Patterns of within-group relatedness are expected to affect the prospects for cooperation among group members through kin selection. It has long been established that dispersal patterns determine the availability of kin and there is ample evidence of matrilineal kin biases in social behavior across primate species. However, in 1979, Jeanne Altmann(1) suggested that mating patterns also influence the structure of within-group relatedness; high male reproductive skew and the frequent replacement of breeding males leads to relatively high levels of paternal relatedness and age-structured paternal sibships within groups. As a consequence of frequent replacement of breeding males, relatedness among offspring of a given female will be reduced to the half- rather than full-sibling level. Depending on the number of sires and degree of relatedness among mothers, members of the same birth cohort may be as closely related as maternal siblings. If animals are able to recognize their paternal kin and exhibit biases in favor of them, this may influence the distribution of cooperation and the intensity of competition within groups of primates. Here, I summarize the evidence that serves as the basis for Altmann's predictions and review evidence regarding whether or not the availability of paternal kin also leads to paternal kin bias among primates.